I would like to disable automatic calculation on a single Google sheet and then have a trigger, either by button or through some implementation of scripts, inserting a column, etc that will allow me to easily recalculate the entire sheet at will, but not automatically.

The is no way to disable the Google Sheets recalculation. The basic workaround is to save the formulas somewhere to be applied every time that you want to calculate the values. Once the calculation finish, use copy then paste as values either by doing this manually or by using a macro/script.

To help me and others to reduce this hassle I published a free Google Sheet add-on that I called Spreadsheet Freezer.